Conventional digital signal processing techniques consider signals that are represented by a set a uniformly spaced sampled values. Although most processing algorithms are derived within a purely discrete framework, there are a variety of biomedical problems (e.g. detection of anatomical structures in images, estimation of velocity from sequences of x-y coordinates) that would be better formulated by considering a signal as a continuous real-valued function defined over some domain. This study is concerned with the development of new processing techniques that represent signals by continuous polynomial spline functions. Traditionally, polynomial spline interpolation or approximation problems are approached using a matrix formulation. Our main contribution has been to recognize that, in the context of signal processing (equally spaced data points), a solution can be obtained by digital filtering. In particular, we have derived recursive filtering structures for the interpolation and least squares approximation of sequences of data points using polynomial splines of any order n. These techniques have been applied to the design of fast algorithms for image interpolation and compression.